It probably is not valid but if you could from a starting cell make your knight jump 80 times into completely different cells with a sequence of 9 different boxes each time then you could have a nice DG variant...

tarek

Last edited by tarek on Fri Nov 17, 2006 3:25 am, edited 1 time in total.

It's maybe possible to make 9 DG each consisting of chain of 9 cells at knight jumps. But some DG will have to share at least 2 cells with a box. eg DG with R1C1 will have to include either R2C3 or R3C2, both in box 1.

Or maybe your idea is to make one big chain of 81 cells at knight jumps with a sequence of warping numbers : 1..9,1..9,... Have no idea if it's feasable, since this is so much constrained. I don't even know if there is such a chain covering all the cells.

Another version : each cell must hold a number consecutive to some other cell at a knight jump. eg if R5C5 = 5, then one of the cells in R37C46 or R46C37 must hold either 4 or 6.

Or else : one and only one consecutive at knight jumps.Or else : both lower & upper consecutives at knight jumps....

Jean-Christophe wrote:Or maybe your idea is to make one big chain of 81 cells at knight jumps with a sequence of warping numbers : 1..9,1..9,... Have no idea if it's feasable, since this is so much constrained. I don't even know if there is such a chain covering all the cells.

One year (and some) ago, I've pondered about the same ideas... A chain covering all 81 cells (a knight's tour on a 9x9 grid) surely exists, but "a sequence of warping numbers" probably not... I've made a few puzzles about the tours/circuits of wazir (orthongonal king), king and knight with absolute minimum numerical sequence of 81 digits in this thread...

Thanks for the input. Will give it a try later using less restrictive rules. There is maybe a knight's tour of consecutive numbers where a sequence of 1-2-1 would be allowed provided it does not break the sudoku rules. Now if it takes 100 years to search...